Memory and Scaling Laws in the Dynamics of Solar Flares

The solar magnetic activity cycle provides energy input that is released in intense bursts of radiation known as solar flares. As such, the dynamics of the activity cycle is embedded in the sequence of times between the flare events. Recent analysis [Snelling et al., 2020, Ashwanden and Johnson, 2021] shows that solar flares exhibit memory on different timescales. Information theory analysis shows that the time ordering of flare events is not random, but rather there is dependence between successive flares. The increased mutual information results from the clustering of flares, which we demonstrate by comparing the cumulative distribution function of successive flares with the cumulative distribution function of surrogate sequences of flares obtained by random permutation of flares within rate-variable Bayesian blocks during which it is assumed that the flare rate is constant. Differences between the cumulative distribution functions is substantial on a timescale around 3 hours, suggesting that flare recurrence on that timescale is more likely than would be expected if the waiting time were drawn from a nonstationary Poisson process. At longer waiting times, the waiting time distribution of flares exhibits a power law form. The power laws also reveal memory in the nonlinear time dependence of the flaring rate. We discuss how time variability in the underlying driver of flares leads to power laws, and in particular discuss how sinusoidal or impulsive driving affects the waiting time distribution of flares.